Combinations and Permutations

Permutations and CombinationsMDM 4U: Mathematics of Data ManagementUnit: Counting and ProbabilityBy: Mr. Allison and Mr. Panchbhaya

Specific ExpectationsLearning GoalsStrand 2.1 Recognize the use of permutations and combinations as counting techniques with advantages over other counting techniquesStrand 2.2Solve simple problems using techniques for counting permutations and combinations, where all objects are distinct

Make connections between, and learn to calculate various permutations and combinationsLearn to behave in class

Agenda of the DayProbability VideoReviewWorksheetGame show Activity

How many combinations would it take for the tire to attach itself back to the car?

Real Life ExamplesVideo game designers to assign appropriate scoring valuesEngineering new products tested rigorously to determine how well they workAllotting numbers for:Credit card numbersCell phone numbersCar plate numbersLottery

FactorialsThe product of all positive integers less than equal or equal to nn! = n x (n 1) x (n 2) x x 2 x 15! =5 x 4 x 3 x 2 x 1 = 120

Permutations

CombinationsCollection of chosen objects for which order does not matter

Speed Round: The sports apparel store at the mall is having a sale. Each customer may choose exactly two items from the list, and purchase them both. The trick is that each 2-item special must have two different items (for example, they may not purchase two T-shirts at the same time). What are all the different combinations that can be made by choosing exactly two items?

15 combinations are possibleQ How many combinations are made if you were purchasing three items instead of two?1. A club of 15 members choose a president, a secretary, and a treasurer in455 ways6 ways2730 ways2. The number of debate teams formed of 6 students out of 10 is:151200210720

3. A student has to answer 6 questions out of 12 in an exam. The first two questions are obligatory. The student has:5040210720

4. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done.564645735756None of the above

5. In how many different ways can the letters of the word LEADING be arranged in such a way that the vowels 3604807205040None of the above

6. How many permutations of 4 different letters are there, chosen from the twenty six letters of the alphabet (repetition is not allowed)?AnswerThe number of permutations of 4 digits chosen from 26 is26P4= 26 25 24 23 = 358,800How many paths are there to the top of the board?

Answer

How many 4 digit numbers can be made using 0-7 with no repeated digits allowed?5040453626881470

Answer= 7x7x6x5 = 1470

First digit of a number can not be 0 No postal code in Canada can begin with the letters D,F,I,O,Q,U, but repeated letters are allowed and any digit is allowed. How many postal codes are possible in Canada?11,657,89013,520,00014,280,00012,240,000Answer= 20x10x26x10x26x10 = 13,520,000

20 choices for the first letter (26 - 6 that cannot be chosen. 10 choices for the digit (0-9). 26 choices for the 3 position (2nd letter) then 10 choice for the 4th positionThen 26 and 10 since you can again repeat numbers and letters.Using digits 0 9, how many 4 digit numbers are evenly divisible by 5 with repeated digits allowed?1400160018001500Answer9 10 10 2 = 1800

First # cant be 0Last # has to be 5 or 0How many ways can you arrange the letters in the word REDCOATS if it must start with a vowel 15,12014,84015,62040,320Answer3* 7 6 5 4 3 2 1 = 15,120

EOA are your 3 choices

How many groups of 3 toys can a child choose to take on a vacation from a toy box containing 11 toys?9901331165286AnswerIf you have a standard deck of cards how many different hands exists of 5 cards2,598,9603,819,816270,725311,875,200AnswerThe game of euchre uses only 24 cards from a standard deck. How many different 5 card euchre hands are possible?7,962,62442,5045,100,48098,280Answer Solve for n 3(nP4) =n-1P581025Answer

How many ways can 3 girls and three boys sit in a row if boys and girls must alternate?AnswerLaura has lost Jordans phone number. All she can remember is that it did not contain a0 or 1 in the first three digits. How many 7 digit #s are possibleAnswer= 8 x 8 x 8 x 10 x 10 x 10 x 10= 5,120,000